88,867 research outputs found
Density Matrix Perturbation Theory
An expansion method for perturbation of the zero temperature grand canonical
density matrix is introduced. The method achieves quadratically convergent
recursions that yield the response of the zero temperature density matrix upon
variation of the Hamiltonian. The technique allows treatment of embedded
quantum subsystems with a computational cost scaling linearly with the size of
the perturbed region, O(N_pert.), and as O(1) with the total system size. It
also allows direct computation of the density matrix response functions to any
order with linear scaling effort. Energy expressions to 4th order based on only
first and second order density matrix response are given.Comment: 4 pages, 2 figure
Canonical density matrix perturbation theory
Density matrix perturbation theory [Niklasson and Challacombe, Phys. Rev.
Lett. 92, 193001 (2004)] is generalized to canonical (NVT) free energy
ensembles in tight-binding, Hartree-Fock or Kohn-Sham density functional
theory. The canonical density matrix perturbation theory can be used to
calculate temperature dependent response properties from the coupled perturbed
self-consistent field equations as in density functional perturbation theory.
The method is well suited to take advantage of sparse matrix algebra to achieve
linear scaling complexity in the computational cost as a function of system
size for sufficiently large non-metallic materials and metals at high
temperatures.Comment: 21 pages, 3 figure
Density Matrix Renormalization Group Lagrangians
We introduce a Lagrangian formulation of the Density Matrix Renormalization
Group (DMRG). We present Lagrangians which when minimised yield the optimal
DMRG wavefunction in a variational sense, both within the general matrix
product ansatz, as well as within the canonical form of the matrix product that
is constructed within the DMRG sweep algorithm. Some of the results obtained
are similar to elementary expressions in Hartree-Fock theory, and we draw
attention to such analogies. The Lagrangians introduced here will be useful in
developing theories of analytic response and derivatives in the DMRG.Comment: 6 page
Vibrational Density Matrix Renormalization Group
Variational approaches for the calculation of vibrational wave functions and
energies are a natural route to obtain highly accurate results with
controllable errors. However, the unfavorable scaling and the resulting high
computational cost of standard variational approaches limit their application
to small molecules with only few vibrational modes. Here, we demonstrate how
the density matrix renormalization group (DMRG) can be exploited to optimize
vibrational wave functions (vDMRG) expressed as matrix product states. We study
the convergence of these calculations with respect to the size of the local
basis of each mode, the number of renormalized block states, and the number of
DMRG sweeps required. We demonstrate the high accuracy achieved by vDMRG for
small molecules that were intensively studied in the literature. We then
proceed to show that the complete fingerprint region of the sarcosyn-glycin
dipeptide can be calculated with vDMRG.Comment: 21 pages, 5 figures, 4 table
The density-matrix renormalization group
The density-matrix renormalization group (DMRG) is a numerical algorithm for
the efficient truncation of the Hilbert space of low-dimensional strongly
correlated quantum systems based on a rather general decimation prescription.
This algorithm has achieved unprecedented precision in the description of
one-dimensional quantum systems. It has therefore quickly acquired the status
of method of choice for numerical studies of one-dimensional quantum systems.
Its applications to the calculation of static, dynamic and thermodynamic
quantities in such systems are reviewed. The potential of DMRG applications in
the fields of two-dimensional quantum systems, quantum chemistry,
three-dimensional small grains, nuclear physics, equilibrium and
non-equilibrium statistical physics, and time-dependent phenomena is discussed.
This review also considers the theoretical foundations of the method, examining
its relationship to matrix-product states and the quantum information content
of the density matrices generated by DMRG.Comment: accepted by Rev. Mod. Phys. in July 2004; scheduled to appear in the
January 2005 issu
Universality of Quantum Information in Chaotic CFTs
We study the Eigenstate Thermalization Hypothesis (ETH) in chaotic conformal
field theories (CFTs) of arbitrary dimensions. Assuming local ETH, we compute
the reduced density matrix of a ball-shaped subsystem of finite size in the
infinite volume limit when the full system is an energy eigenstate. This
reduced density matrix is close in trace distance to a density matrix, to which
we refer as the ETH density matrix, that is independent of all the details of
an eigenstate except its energy and charges under global symmetries. In two
dimensions, the ETH density matrix is universal for all theories with the same
value of central charge. We argue that the ETH density matrix is close in trace
distance to the reduced density matrix of the (micro)canonical ensemble. We
support the argument in higher dimensions by comparing the Von Neumann entropy
of the ETH density matrix with the entropy of a black hole in holographic
systems in the low temperature limit. Finally, we generalize our analysis to
the coherent states with energy density that varies slowly in space, and show
that locally such states are well described by the ETH density matrix.Comment: 43 page
Density Matrix in Quantum Mechanics and Distinctness of Ensembles Having the Same Compressed Density Matrix
We clarify different definitions of the density matrix by proposing the use
of different names, the full density matrix for a single-closed quantum system,
the compressed density matrix for the averaged single molecule state from an
ensemble of molecules, and the reduced density matrix for a part of an
entangled quantum system, respectively. We show that ensembles with the same
compressed density matrix can be physically distinguished by observing
fluctuations of various observables. This is in contrast to a general belief
that ensembles with the same compressed density matrix are identical. Explicit
expression for the fluctuation of an observable in a specified ensemble is
given. We have discussed the nature of nuclear magnetic resonance quantum
computing. We show that the conclusion that there is no quantum entanglement in
the current nuclear magnetic resonance quantum computing experiment is based on
the unjustified belief that ensembles having the same compressed density matrix
are identical physically. Related issues in quantum communication are also
discussed.Comment: 26 pages. To appear in Foundations of Physics, 36 (8), 200
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